A multiple choice test has 20 items with four possible answers given for each item. 12 is the minimum passing score.
a) What is the probability of passing simply by guessing?
b) What is the probability of passing if you are able to eliminate one choice each time but guess among the remaining three choices?
c) Suppose the questions come from a large test bank and you know the correct answer to 50% of the questions in the test bank, can eliminate one choice for 40% of the questions, and have to guess blindly for the other 10% of the questions. If the questions are selected from the test bank independently at random, what is the probability that you pass the test?